Final answer:
To calculate the total interest cost using the U.S. Rule with ordinary interest, we find the interest over given time periods before and after partial payments and sum them up. The balances after payments on the 100th and 180th days are recalculated following each payment.
Step-by-step explanation:
To solve for the total interest cost using the U.S. Rule and given the principal, interest rate, and time with partial payments, we proceed step by step.
The ordinary interest for the loan before any payments is calculated using the formula:
Total interest = (Principal × Rate × Time) / 360
For the initial 100 days:
Total interest = ($9,000 × 0.06 × 100) / 360 = $150.
On the 100th day, after a partial payment of $3,200, the new principal becomes $9,000 - $3,200 = $5,800.
The interest on the new principal for the next 80 days (until the 180th day) is:
Total interest = ($5,800 × 0.06 × 80) / 360 = $77.33
On the 180th day, after a partial payment of $2,200, the new principal becomes $5,800 - $2,200 = $3,600.
The interest on the new principal for the remaining 60 days (until the 240th day) is:
Total interest = ($3,600 × 0.06 × 60) / 360 = $36.00
The total interest cost is the sum of all interest amounts calculated for each period before payments are made:
Total interest cost = $150 + $77.33 + $36.00 = $263.33
Therefore, the balances after each payment are:
Balance after the payment on the 100th day is $5,800 with an interest of $150 accrued by that time.
Balance after the payment on the 180th day is $3,600 with an additional interest of $77.33 accrued between the 100th and 180th day.